Identifying vertical, horizontal asymptotes and holes

👉 Learn how to find the vertical/horizontal asymptotes of a function. An asymptote is a line that the graph of a function approaches but never touches. The vertical asymptote is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptote(s) of a rational function, we set the denominator equal to 0 and solve for x.

The horizontal asymptote is a horizontal line which the graph of the function approaches but never crosses (though they sometimes cross them). A rational function has a horizontal asymptote of y = 0 when the degree of the numerator is less than the degree of the denominator. A rational function has a horizontal asymptote of y = c, (where c is the quotient of the leading coefficient of the numerator and that of the denominator) when the degree of the numerator is equal to the degree of the denominator. A rational function has no horizontal asymptote if the degree of the numerator is greater than the degree of the denominator.

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Organized Videos:
✅ Find the Asymptotes of Rational Functions
   • Find the Asymptotes of Rational Functions  
✅ Find the Vertical and Horizontal Asymptotes of a Rational Function y=0
   • Find the Vertical and Horizontal Asymptote...  
✅ Asymptotes of Rational Functions | Learn About
   • Asymptotes of Rational Functions | Learn A...  
✅ Find the Asymptotes of a Rational Function with Trig
   • Find the Asymptotes of a Rational Function...  
✅ Find the Asymptotes and Holes of a Rational Function
   • Find the Asymptotes and Holes of a Rationa...  
✅ Find the Slant Asymptotes of the Rational Function
   • Find the Slant Asymptotes of the Rational ...  

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